We can start the discussion on soldering irons, I guess.
There seem to be two main strategies. I'm not super well versed on the pro's & cons of each. A lot of soldering irons use a resistive heating element. Dump current in, get heat. Higher end soldering irons tend to use high frequency inductive heating. Hakko has a write up here[1].
Agreed that for a switching supply, PPS isn't going to help a lot. For a resistive soldering iron, a PPS capable USB power source would be very helpful. All that's needed is a control loop, to monitor temperature & adjust the asked for input voltage and/or current.
Honestly not sure what the Pinecil or the well known TS100 soldering iron are, resistive or RF inductive. It'd be great if they were RF inductive heating, & PPS wasn't helpful, as the much finer control would be great. I hadn't considered that they could be.
[1] https://www.hakko.com/english/products/hakko_fx100.html